Reply to: Animal magnetic sensitivity and magnetic displacement experiments

In their matters arising article

however, have enormous sample sizes (n = 2996 and n = 17,799), and hence, the effects reported might reflect shifts in the mean position of a tight but long-tailed distribution.This way, even a 0.01-degree shift in inclination might be detected hundreds of kilometres away since the long-tailed distribution's movement might be minimal (since sensitivity is low), yet a statistical trend might be observed given the large sample size (see Fig. 1).
Secondly, sensitivity assessed via philopatric accuracy might differ markedly from the actual physical sensitivity of a system.In much the same way that the winning guess of 'number of jelly beans in the jar' is often astonishingly accurate-despite each participant's ability to count beans being relatively poor-repeated estimations of position using a noisy magnetoreceptor can give the impression of accuracy far beyond that predicted by its physical sensitivity.Indeed, a simple simulation using normally distributed noise suggests that a sensor with a sensitivity of 0.6°can achieve a functional sensitivity of 0.05°by measuring the magnetic field instantaneously once a day for 100 days (an increase in accuracy of more than an order of magnitude; see Fig. 1).This could explain the magnetic imprinting observed in birds, where a protracted post-fledging period is almost guaranteed.Such an ability would not, however, explain responses to virtual displacement; these experiments lack the repeated sampling required to improve sensitivity using central tendency.
Thirdly, during a virtual magnetic displacement, the subject animal experiences a constant magnetic field.Importantly, there is no opportunity for the animal to move and experience alterations in the field that may allow it to take multiple readings and gain an impression of gradients of change and, therefore, discriminate between minimal signals.If one imagines a test in which someone puts their hand into a bath of warm water for several minutes, removes it, waits several hours, then puts the hand into a new bath of water with a difference of 1 °C, and then determines which bath was hotter-it would be an extremely difficult test.If, instead, there was a single bath of water, and in one end it was 1 °C hotter than the other, then by moving the hand back and forth in the bath it would be relatively easy to determine which is the hotter end.In both scenarios the sensitivity of the hand is the same, but the test in the first is far more challenging.The first (difficult) scenario is comparable to the opportunity provided to an animal when it has been virtually magnetically displaced and is required to determine the parameters of the field.In contrast, the second scenario allows for  https://doi.org/10.1038/s42003-024-06270-x the possibility of sensing gradients of change.All of the citations that Lohmann et al. provide as evidence for higher sensitivity values than those we used are relevant only to animals that were allowed to experience gradients of change of magnetic fields [1][2][3][4][5][6][7][8][9][10] .Therefore, they are not relevant to how sensitive an animal may be to a virtual magnetic displacement.
It is, then, unclear from the literature what our expectation of sensitivity to magnetic displacement is expected to be for any taxa.This, in turn, increases the utility of the tool presented in our original manuscript since, given this ambiguity, it is perhaps better to be safe than sorry.Nonetheless, whilst we believe that the parameters presented in our original manuscript represent a 'best case' for magnetic sensitivity (it is hard to imagine, based on other sensory inputs, a sub-1-degree sensitivity, or sensitivity below the daily secular variation of the geomagnetic field), it is perhaps worth considering how virtual displacement might function under an assumption of extremely high sensitivity (far higher than we believe there is evidence for).To that end, our tool demonstrates that even in such instances many possible locations can still exist spanning a very large geographic area.For example, Fig. 2 shows that even if animals are sensitive to 0.05°of inclination and 20 nT of intensity, there are locations spanning the width of the mid-Atlantic Ocean (locations, for example, that are highly relevant to the movements of loggerhead turtles), and in the Gulf of Mexico and Western Pacific Ocean, that all have the same magnetic values (red dots in Fig. 2).We might conclude, therefore, that (a) an of absolute magnetoreceptive sensitivity requires further research going forward using a different paradigm to behavioural responses to changes in the magnetic field and, (b) that irrespective of sensitivity, extreme care must be taken when conceptualising and interpreting behavioural responses to virtual displacement.

Fig. 1 |
Fig. 1 | Magnetic secular variation and philopatry.a-d A schematic demonstrating how slight magnetic secular variation might cause changes in distribution even in animals with low-resolution magnetoreceptors.In Case a, the magnetic field has shifted left slightly, causing a drop in recovery probability at the starred location even though most animals return to the natal site (owing to the tight distribution caused by low magnetic sensitivity).Case b is intermediate, whilst Case c shows the opposite phenomenon; the field has shifted right, and a response can be recorded at the starred site even though the sensitivity of any given animal is very low.e A simulation showing how even noisy sensors can achieve remarkably accurate philopatry (<0.05 degrees) through repeated sampling of the magnetic field.Each point represents 100 simulations where the magnetic field is sampled n times with both sensor error and local secular variation.Whiskers represent standard deviation.Magnetic data is derived from the Hartland Magnetic Observatory (UK).

Fig. 2 |
Fig. 2 | Multiple possible virtual displacement locations with high sensitivity assumed.Red dots indicate all the locations that share the same magnetic parameters (magnetic total intensity = 45083 nT, magnetic inclination = 56.42degrees) with a sensitivity assumption of ±20 nT for magnetic intensity, and ±0.05 degrees for magnetic inclination.Magnetic values obtained from the IGRF for May 2020.